SOLUTION: Hi, my name is Grace Rogers and I am having trouble finding the symmetries of y = cuberoot of x How do I know if its symmetrical?? your help is greatly appreciated!

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Hi, my name is Grace Rogers and I am having trouble finding the symmetries of y = cuberoot of x How do I know if its symmetrical?? your help is greatly appreciated!      Log On


   

Question 842193: Hi, my name is Grace Rogers and I am having trouble finding the symmetries of
y = cuberoot of x
How do I know if its symmetrical??
your help is greatly appreciated!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f(-x) is equal to -f(x) so it's symmetrical about the origin.

the graph of your equation can be seen below:

$$$

the test for symmetry is generally the following:

if f(-x) = f(x), then the equation is symmetrical about the y-axis.

if f(-x) = -f(x), then the equation is symmetrical about the origin.

if the root is even then (f(-x) will not be equal to -f(x).

if the root is odd, then (f(-x) will be equal to -f(x).

cube root of (-27) is equal to -3.
minus cube root of 27 is equal to minus 3 which is equal to -3.
they are equal.

square root of (-25) is equal to 5i.
minus square root of (25) is equal to -5.
they are not equal.